This is a valid concern for many clients. I can see how in some cases it'd be impossible to work with the therapist whose political views are very different from your own. I elaborate on this topic in my article here Therapy Consumer Guide - Therapy and Politics

For me the decision to work with the therapist with the different political views would be based on whether I believe their views reflect some deeper moral values or not. Our political positions may or may not reflect our values. I know people with whom I disagree politically who have the same values as I do, but they see the solutions to the societal problems differently from how I see them. I believe their views are based on a lack of education about history and economy, not on a lack of morality or social consciousness. I am pretty sure they think the same about me. With those people I try to continue a dialog no matter how much their views may piss me off.

There are others, however, whose values are clearly different from mine. With those I have nothing to discuss. I know they will follow what they want to follow no matter what I say. If I had a feeling that my therapist was one of those, I would look for a new therapist.

So, it depends..